$11^{2}_{6}$ - Minimal pinning sets
Pinning sets for 11^2_6 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_6 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 64
of which optimal: 1
of which minimal: 1
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.83846
on average over minimal pinning sets: 2.0
on average over optimal pinning sets: 2.0
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 4, 5, 8}
5
[2, 2, 2, 2, 2]
2.00
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
1
0
0
2.0
6
0
0
6
2.39
7
0
0
15
2.67
8
0
0
20
2.88
9
0
0
15
3.04
10
0
0
6
3.17
11
0
0
1
3.27
Total
1
0
63
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 4, 4, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,5,0],[0,6,6,7],[0,8,4,4],[1,3,3,8],[1,7,6,6],[2,5,5,2],[2,5,8,8],[3,7,7,4]]
PD code (use to draw this multiloop with SnapPy): [[4,18,1,5],[5,3,6,4],[8,17,9,18],[1,11,2,12],[12,2,13,3],[6,15,7,16],[16,7,17,8],[9,15,10,14],[10,13,11,14]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (5,4,-6,-1)(12,1,-13,-2)(9,14,-10,-15)(3,18,-4,-5)(17,6,-18,-7)(7,16,-8,-17)(13,8,-14,-9)(15,10,-16,-11)(2,11,-3,-12)
Edge permutation $\epsilon=$ (-1,1)(-2,2)(-3,3)(-4,4)(-5,5)(-6,6)(-7,7)(-8,8)(-9,9)(-10,10)(-11,11)(-12,12)(-13,13)(-14,14)(-15,15)(-16,16)(-17,17)(-18,18)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,12,-3,-5)(-2,-12)(-4,5)(-6,17,-8,13,1)(-7,-17)(-9,-15,-11,2,-13)(-10,15)(-14,9)(-16,7,-18,3,11)(4,18,6)(8,16,10,14)
Multiloop annotated with half-edges
11^2_6 annotated with half-edges